Analysis of xx-top500-293-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 2..7......5.....3.......2......13.5.4.....6............13.....4..46.........29... initial

Autosolve

position: 23.7...4..5.142.3.14.3..2...62.1345.4..2..6.33...64..2613...924924631...5..4293.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 6,9 => CTR => C3: 7,8
* DIS # C3: 6,9 => CTR => C3: 7,8
* PRF # B6: 9 => SOL
* DIS # I4: 9 => CTR => I4: 7,8
* DIS # B6: 7 => CTR => B6: 8,9
* DIS # I4: 7 => CTR => I4: 8,9
* PRF # B6: 9 => SOL
* DIS # C3: 6,9 => CTR => C3: 7,8
* DIS # D6: 9 => CTR => D6: 5,8
* CNT   9 HDP CHAINS /  38 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # C3: 6,9 => CTR => C3: 7,8
* PRF C3: 7,8 # B6: 9 => SOL
* STA C3: 7,8 + B6: 9
* CNT   2 HDP CHAINS /  11 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

2..7......5.....3.......2......13.5.4.....6............13.....4..46.........29... initial
23.7...4..5.142.3.14.3..2...62.1345.4..2..6.33...64..2613...924924631...5..4293.. autosolve
239756841856142739147398265762913458481275693395864172613587924924631587578429316 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
A2: 7,8
C2: 6,9
G2: 7,8
I2: 6,9
A4: 7,8
B5: 8,9
C5: 1,5
C6: 1,5
D4: 8,9
B9: 7,8
C9: 7,8
D7: 5,8
H8: 7,8
H9: 1,6
I9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G1,I1: 1.. / G1 = 1  => 15 pairs (_) / I1 = 1  => 18 pairs (_)
C5,C6: 1.. / C5 = 1  => 18 pairs (_) / C6 = 1  => 17 pairs (_)
H9,I9: 1.. / H9 = 1  => 18 pairs (_) / I9 = 1  => 15 pairs (_)
C5,H5: 1.. / C5 = 1  => 18 pairs (_) / H5 = 1  => 17 pairs (_)
G1,G6: 1.. / G1 = 1  => 15 pairs (_) / G6 = 1  => 18 pairs (_)
I1,I9: 1.. / I1 = 1  => 18 pairs (_) / I9 = 1  => 15 pairs (_)
C5,C6: 5.. / C5 = 5  => 17 pairs (_) / C6 = 5  => 18 pairs (_)
G8,I8: 5.. / G8 = 5  => 17 pairs (_) / I8 = 5  => 20 pairs (_)
C6,D6: 5.. / C6 = 5  => 18 pairs (_) / D6 = 5  => 17 pairs (_)
D6,D7: 5.. / D6 = 5  => 17 pairs (_) / D7 = 5  => 18 pairs (_)
G1,G8: 5.. / G1 = 5  => 20 pairs (_) / G8 = 5  => 17 pairs (_)
F1,F3: 6.. / F1 = 6  => 17 pairs (_) / F3 = 6  => 16 pairs (_)
H9,I9: 6.. / H9 = 6  => 15 pairs (_) / I9 = 6  => 18 pairs (_)
C2,I2: 6.. / C2 = 6  => 15 pairs (_) / I2 = 6  => 14 pairs (_)
H3,H9: 6.. / H3 = 6  => 18 pairs (_) / H9 = 6  => 15 pairs (_)
A2,C3: 7.. / A2 = 7  =>  0 pairs (X) / C3 = 7  => 17 pairs (_)
A4,B6: 7.. / A4 = 7  => 17 pairs (_) / B6 = 7  =>  0 pairs (X)
E5,F5: 7.. / E5 = 7  => 17 pairs (_) / F5 = 7  => 17 pairs (_)
B9,C9: 7.. / B9 = 7  => 17 pairs (_) / C9 = 7  =>  0 pairs (X)
E7,F7: 7.. / E7 = 7  => 17 pairs (_) / F7 = 7  => 17 pairs (_)
A2,G2: 7.. / A2 = 7  =>  0 pairs (X) / G2 = 7  => 17 pairs (_)
A4,I4: 7.. / A4 = 7  => 17 pairs (_) / I4 = 7  =>  0 pairs (X)
A2,A4: 7.. / A2 = 7  =>  0 pairs (X) / A4 = 7  => 17 pairs (_)
B6,B9: 7.. / B6 = 7  =>  0 pairs (X) / B9 = 7  => 17 pairs (_)
C3,C9: 7.. / C3 = 7  => 17 pairs (_) / C9 = 7  =>  0 pairs (X)
E5,E7: 7.. / E5 = 7  => 17 pairs (_) / E7 = 7  => 17 pairs (_)
F5,F7: 7.. / F5 = 7  => 17 pairs (_) / F7 = 7  => 17 pairs (_)
B9,C9: 8.. / B9 = 8  =>  0 pairs (X) / C9 = 8  => 17 pairs (_)
A2,G2: 8.. / A2 = 8  => 17 pairs (_) / G2 = 8  =>  0 pairs (X)
A2,A4: 8.. / A2 = 8  => 17 pairs (_) / A4 = 8  =>  0 pairs (X)
E1,E3: 9.. / E1 = 9  => 17 pairs (_) / E3 = 9  => 17 pairs (_)
B5,B6: 9.. / B5 = 9  => 16 pairs (_) / B6 = 9  =>  0 pairs (*)
D4,D6: 9.. / D4 = 9  => 16 pairs (_) / D6 = 9  =>  0 pairs (X)
C2,I2: 9.. / C2 = 9  => 14 pairs (_) / I2 = 9  => 15 pairs (_)
D4,I4: 9.. / D4 = 9  => 16 pairs (_) / I4 = 9  =>  0 pairs (X)
B5,H5: 9.. / B5 = 9  => 16 pairs (_) / H5 = 9  =>  0 pairs (*)
* DURATION: 0:01:09.884773  START: 12:58:16.807795  END: 12:59:26.692568 2017-05-04
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B5,B9,C2,C5,C6,C9,D4,D7,G2,H8,H9,I2,I9)
* 23.7...4..5.142.3.14.3..2...62.1345.4..2..6.33...64..2613...924924631...5..4293..
* PAIR A2: 7,8 BLK 1
C3: 7,8,6,9                              # reduction candidate for 7,8
C3: 6,9 => CTR
* 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5..4293..
C3: 7,8                                  # 17 pairs
* PAIR C2: 6,9 BLK 1
C1: 6,9,8                                # reduction candidate for 6,9
C1: 6,9                                  # 17 pairs
C3: 6,9,7,8                              # reduction candidate for 6,9
C3: 6,9 => CTR
* 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5..4293..
C3: 7,8                                  # 17 pairs
* PAIR G2: 7,8 BLK 3
H3: 7,8,6,9                              # reduction candidate for 7,8
H3: 7,8                                  # 19 pairs
I3: 7,8,5,6,9                            # reduction candidate for 7,8
I3: 7,8                                  # 21 pairs
* PAIR G2: 7,8 COL G
G6: 7,8,1                                # reduction candidate for 7,8
G6: 7,8                                  # 15 pairs
G8: 7,8,5                                # reduction candidate for 7,8
G8: 7,8                                  # 20 pairs
* PAIR I2: 6,9 BLK 3
I1: 6,9,1,5,8                            # reduction candidate for 6,9
I1: 6,9                                  # 22 pairs
H3: 6,9,7,8                              # reduction candidate for 6,9
H3: 6,9                                  # 16 pairs
I3: 6,9,5,7,8                            # reduction candidate for 6,9
I3: 6,9                                  # 22 pairs
* PAIR A4: 7,8 BLK 4
B6: 7,8,9                                # reduction candidate for 7,8
B6: 9 => SOLVED
* 239756841856142739147398265762913458481275693395864172613587924924631587578429316
B6: 7,8                                  # 16 pairs
* PAIR A4: 7,8 ROW 4
I4: 7,8,9                                # reduction candidate for 7,8
I4: 9 => CTR
* 23.7...4.8591427361473.629.7628134594912..6833859641.26135..924924631.7.5784293..
I4: 7,8                                  # 16 pairs
* PAIR B5: 8,9 BLK 4
B6: 8,9,7                                # reduction candidate for 8,9
B6: 7 => CTR
* 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5874293..
B6: 8,9                                  # 17 pairs
* PAIR B5: 8,9 ROW 5
H5: 8,9,1                                # reduction candidate for 8,9
H5: 8,9                                  # 18 pairs
H5: 1                                    # 17 pairs
* PAIR D4: 8,9 BLK 5
D6: 8,9,5                                # reduction candidate for 8,9
D6: 8,9                                  # 18 pairs
D6: 5                                    # 17 pairs
* PAIR D4: 8,9 ROW 4
I4: 8,9,7                                # reduction candidate for 8,9
I4: 7 => CTR
* 23.7...4.75.14283.14.3..27.86291345749.2..68337..64.92613...924924631...5874293..
I4: 8,9                                  # 17 pairs
* PAIR B9: 7,8 COL B
B6: 7,8,9                                # reduction candidate for 7,8
B6: 9 => SOLVED
* 239756841856142739147398265762913458481275693395864172613587924924631587578429316
B6: 7,8                                  # 16 pairs
* PAIR C9: 7,8 COL C
C3: 7,8,6,9                              # reduction candidate for 7,8
C3: 6,9 => CTR
* 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5..4293..
C3: 7,8                                  # 17 pairs
* PAIR D7: 5,8 BLK 8
E7: 5,8,7                                # reduction candidate for 5,8
E7: 5,8                                  # 17 pairs
F7: 5,8,7                                # reduction candidate for 5,8
F7: 5,8                                  # 17 pairs
* PAIR D7: 5,8 COL D
D6: 5,8,9                                # reduction candidate for 5,8
D6: 9 => CTR
* 23.7...4.8591427361473.629.7628134594912..6833859641.26135..924924631.7.5784293..
D6: 5,8                                  # 16 pairs
* PAIR H8: 7,8 BLK 9
G8: 7,8,5                                # reduction candidate for 7,8
G8: 7,8                                  # 20 pairs
I8: 7,8,5                                # reduction candidate for 7,8
I8: 7,8                                  # 17 pairs
* PAIR H8: 7,8 COL H
H3: 7,8,6,9                              # reduction candidate for 7,8
H3: 7,8                                  # 19 pairs
H6: 7,8,1,9                              # reduction candidate for 7,8
H6: 7,8                                  # 18 pairs
* PAIR I9: 1,6 COL I
I1: 1,6,5,8,9                            # reduction candidate for 1,6
I1: 1,6                                  # 16 pairs
I1: 5,8,9                                # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-293-base-pr-000.dot
* REASONING
* DIS # C3: 6,9 => CTR => C3: 7,8
* DIS # C3: 6,9 => CTR => C3: 7,8
* PRF # B6: 9 => SOL
* DIS # I4: 9 => CTR => I4: 7,8
* DIS # B6: 7 => CTR => B6: 8,9
* DIS # I4: 7 => CTR => I4: 8,9
* PRF # B6: 9 => SOL
* DIS # C3: 6,9 => CTR => C3: 7,8
* DIS # D6: 9 => CTR => D6: 5,8
* CNT   9 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B5,B9,C2,C5,C6,C9,D4,D7,G2,H8,H9,I2,I9)
* 23.7...4..5.142.3.14.3..2...62.1345.4..2..6.33...64..2613...924924631...5..4293..
* PAIR A2: 7,8 BLK 1
C3: 7,8,6,9                              # reduction candidate for 7,8
C3: 6,9 => CTR
* 23.7...4.75.14283.14.3..2..86291345749.2..6.337..64192613...92492463178.5..4293..
* PAIR G2: 7,8 BLK 3
H3: 7,8,6,9                              # reduction candidate for 7,8
H3: 7,8                                  # 23 pairs
I3: 7,8,5,6,9                            # reduction candidate for 7,8
I3: 7,8                                  # 25 pairs
* PAIR G2: 7,8 COL G
G6: 7,8,1                                # reduction candidate for 7,8
G6: 7,8                                  # 17 pairs
G8: 7,8,5                                # reduction candidate for 7,8
G8: 7,8                                  # 14 pairs
* PAIR I2: 6,9 BLK 3
I1: 6,9,1,5,8                            # reduction candidate for 6,9
I1: 6,9                                  # 24 pairs
H3: 6,9,7,8                              # reduction candidate for 6,9
H3: 6,9                                  # 18 pairs
I3: 6,9,5,7,8                            # reduction candidate for 6,9
I3: 6,9                                  # 26 pairs
* PAIR A4: 7,8 BLK 4
B6: 7,8,9                                # reduction candidate for 7,8
B6: 9 => SOLVED
* 239756841856142739147398265762913458481275693395864172613587924924631587578429316
* DURATION: 0:00:13.049552  START: 13:00:06.722108  END: 13:00:19.771660 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-293-base-pr-001.dot
* REASONING
* DIS # C3: 6,9 => CTR => C3: 7,8
* PRF C3: 7,8 # B6: 9 => SOL
* STA C3: 7,8 + B6: 9
* CNT   2 HDP CHAINS /  11 HYP OPENED

Header Info

Top 500 Minimum 17 293

solution: 239756841856142739147398265762913458481275693395864172613587924924631587578429316
info: 2404     FNBTHWXY S8.f     48963

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 239756841856142739147398265762913458481275693395864172613587924924631587578429316 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # C3: 7,8 => UNS
* DIS # C3: 6,9 => CTR => C3: 7,8
* INC # C1: 6,9 => UNS
* DIS # C3: 6,9 => CTR => C3: 7,8
* INC # C3: 7,8 => UNS
* INC # H3: 7,8 => UNS
* INC # I3: 7,8 => UNS
* INC # G6: 7,8 => UNS
* INC # G8: 7,8 => UNS
* INC # I1: 6,9 => UNS
* INC # H3: 6,9 => UNS
* INC # I3: 6,9 => UNS
* INC # B6: 7,8 => UNS
* PRF # B6: 9 => SOL
* INC # I4: 7,8 => UNS
* DIS # I4: 9 => CTR => I4: 7,8
* INC # B6: 8,9 => UNS
* DIS # B6: 7 => CTR => B6: 8,9
* INC # H5: 8,9 => UNS
* INC # H5: 1 => UNS
* INC # D6: 8,9 => UNS
* INC # D6: 5 => UNS
* INC # I4: 8,9 => UNS
* DIS # I4: 7 => CTR => I4: 8,9
* INC # B6: 7,8 => UNS
* PRF # B6: 9 => SOL
* INC # C3: 7,8 => UNS
* DIS # C3: 6,9 => CTR => C3: 7,8
* INC # E7: 5,8 => UNS
* INC # F7: 5,8 => UNS
* INC # D6: 5,8 => UNS
* DIS # D6: 9 => CTR => D6: 5,8
* INC # G8: 7,8 => UNS
* INC # I8: 7,8 => UNS
* INC # H3: 7,8 => UNS
* INC # H6: 7,8 => UNS
* INC # I1: 1,6 => UNS
* INC # I1: 5,8,9 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C3: 7,8 => UNS
* DIS # C3: 6,9 => CTR => C3: 7,8
* INC C3: 7,8 # H3: 7,8 => UNS
* INC C3: 7,8 # I3: 7,8 => UNS
* INC C3: 7,8 # G6: 7,8 => UNS
* INC C3: 7,8 # G8: 7,8 => UNS
* INC C3: 7,8 # I1: 6,9 => UNS
* INC C3: 7,8 # H3: 6,9 => UNS
* INC C3: 7,8 # I3: 6,9 => UNS
* INC C3: 7,8 # B6: 7,8 => UNS
* PRF C3: 7,8 # B6: 9 => SOL
* STA C3: 7,8 + B6: 9
* CNT  11 HDP CHAINS /  11 HYP OPENED